Enhanced matrix symbol error correction method

ABSTRACT

A system and method for error correction for machine-readable symbols having data codewords, and having error correction (EC) codewords derived from the data codewords and redundantly indicating the location and data contents of the data codewords. The symbols use Reed-Solomon (RS) error correction to retrieve damaged codewords. RS error correction normally requires two EC codewords to identify both the location and data contents of a data codeword. The present system and method performs optical contrast analysis on the codewords, identifying those codewords with the lowest contrast levels (that is, the least difference between the reflectance of the black or white cells and the black/white threshold). Codewords with the lowest contrast levels are flagged as optically ambiguous, thereby marking, in the EC equations, the locations of the codewords most like to be in error. As a result, only a single EC codeword is required to retrieve the data for a flagged data codeword.

FIELD OF THE INVENTION

The present invention relates to a method and apparatus for decoding machine-readable symbols, and more particularly, to a method and apparatus for decoding symbols requiring error correction.

BACKGROUND

Machine-readable symbols provide a means for encoding information in a compact printed form (or embossed form) which can be scanned and then interpreted by an optical-based symbol detector. Such machine readable symbols are often attached to (or impressed upon) product packaging, food products, general consumer items, machine parts, equipment, and other manufactured items for purposes of machine-based identification and tracking.

One exemplary type of machine-readable symbol is a bar code that employs a series of bars and white spaces vertically oriented along a single row. Groups of bars and spaces correspond to a codeword. The codeword is associated with an alpha-numeric symbol, one or more numeric digits, or other symbol functionality.

To facilitate encoding of greater amounts of information into a single machine-readable symbol, two-dimensional bar codes have been devised. These are also commonly referred to as stacked, matrix and/or area bar codes. Examples of such two-dimensional symbologies include Data Matrix, Code One, PDF-417, MaxiCode, QR Code, and Aztec Code. 2D matrix symbologies employ arrangements of regular polygon-shaped cells (also called elements or modules) where the center to center distance of adjacent elements is uniform. Typically, the polygon-shaped cells are squares. The specific arrangement of the cells in 2D matrix symbologies represents data characters and/or symbology functions.

As an example of a 2D matrix symbol technology, a Data Matrix code is a two-dimensional matrix barcode consisting of high-contrast “cells” (typically black and white cells) or modules arranged in either a square or rectangular pattern. The information to be encoded can be text or numeric data, or control symbols. The usual data size ranges from a few bytes up to 1556 bytes. Specific, designated, standardized groups of cells—typically eight cells—are each referred to as a “symbol character.” The symbol characters have values which are referred to as “codewords.” With a black cell interpreted as a 0 (zero) and a white cell interpreted as a 1 (one), an eight-cell codeword can code for numbers 0 through 255; in turn, these numeric values can be associated with alphanumeric symbols through standard codes such as ASCII, EBCDIC, or variations thereon, or other functionality.

The codewords—that is, the designated groups of cells in a symbol—have specific, standardized positions within the overall symbol. The interpretation of a symbol in a given context (for example, for a given manufacturer and/or a given product) therefore depends on the codewords within the symbol; and in particular, the interpretation depends on both: (i) the contents of each codeword (that is, the pattern of cells in each codeword), and (ii) the placement or position of each codeword in the symbol.

Typically, for sequential alphanumeric data (for example, a product identification number or a street address), each sequential data character is assigned to the symbols of a codeword in a standardized order. For example, the order may be left-to-right along the rows of the symbol, or according to a standardized diagonal pattern of placement. Because the codewords have specific, standards-specified placements within a symbol—and because no information about the placement is contained in the symbol character—the symbols may also be referred to as “matrix symbols” or “matrix symbology barcodes.”

Bar code readers are employed to read the matrix symbols using a variety of optical scanning electronics and methods. Ideally, the machine-readable symbols which are scanned by a bar code reader are in perfect condition, with all of the cells of consistent, uniform size; each cell being fully filled with either total black or total white; and the contrast between black and white cells being 100%.

In real, practical application the machine-readable symbols which are scanned by a bar code reader may be imperfect. They may be smudged by external substances (grease, dirt, or other chemicals in the environment); or the surface on which the symbols were printed may be stretched, compressed, or torn; or the printing process itself may be flawed (for example, due to low ink levels in a printer, clogged printheads, etc.). The defects in actual symbols may introduce errors in the machine reading process.

To address these practical problems, error correction techniques are often used to increase reliability: even if one or more cells are damaged so as to make a codeword unreadable, the unreadable codeword can be recovered through the error-correction process, and the overall message of the symbol can still be read.

For example, machine-readable symbols based on the Data Matrix ECC 200 standard employ Reed-Solomon codes for error and erasure recovery. ECC 200 allows the routine reconstruction of the entire encoded data string when the symbol has sustained 25% damage (assuming the matrix can still be accurately located).

Under this standard, approximately half the codewords in a symbol are used directly for the data to be represented, and approximately half the codewords are used for error correction. The error-correction (EC) symbols are calculated using a mathematical tool know as the Reed-Solomon algorithm. The codewords for the symbol are the input to the Reed-Solomon algorithm, and the error-correction (EC) symbols are the output of the Reed-Solomon algorithm. The complete machine-readable symbol includes both the data codewords and the EC codewords.

For a given symbol format (such as Data Matrix, PDF-417, QR-Code, Aztec Code, and others), and for a given size of the symbol matrix, there are a fixed, designated numbers of EC codewords. To recover any one, particular damaged (unreadable) codeword, two things must be recovered: (i) the location of the damaged data codeword within the symbol, and (ii) the contents (the bit pattern) of the damaged data codeword. In turn, to recover both the location and the bit pattern for a single codeword requires two of the available EC symbols. It follows that if a machine-readable symbol has two damaged codewords, four EC codewords are required to recover the full symbol. Generally, if a symbol has “N” damaged codewords, then 2*N EC codewords are required to recover the full symbol.

The number of EC codewords in a symbol is limited. This places a limit on the number of damaged, unreadable data codewords which can be recovered. Generally with error correction techniques, and using present methods, the number of damaged data codewords which can be recovered is half the total number of EC codewords. For example, in a Data Matrix symbol with 16×16 cells, the total number of EC codewords is 12. This means that at most 6 damaged data codewords can be recovered. If more than 6 of the data codewords are damaged, the complete symbol may be unreadable.

However, if the location of the data codeword in error is already known, then only one EC codeword is needed to correct the error. This technique is called “erasure decoding”. Unfortunately, in Matrix Code symbols generally, the location of the errors is not known.

Therefore, there exists a need for a system and method for recovering more damaged data codewords in a symbol than may be recovered based on only the error-correcting symbols by themselves. More particularly, what is needed is a system and method for determining the location of a damaged or erroneous data codeword, independent of the information stored in the EC codewords.

SUMMARY

Accordingly, in one aspect, the present invention solves the problem of not being able to use erasure decoding with matrix symbologies by evaluating the gray-level information available in the scanner and keeping track of those codewords with the least contrast difference. The decoder then utilizes erasure decoding on these least-contrast codewords. Since the location of the erroneous data codewords has been estimated via the contrast detection, only one EC codeword is required to recover the data in the damaged codeword. (And so, only one EC codeword is required to fully recover the damaged data codeword, both its location and data.)

Because only one EC codeword is required instead of two, more EC codewords remain unused and available for decoding other possible errors. This increases the total number of data codewords that can be corrected. This is particularly useful in applications where symbols get dirty (e.g. automotive assembly), damaged (e.g. supply chain), have specular components (e.g. direct part marking (DPM)) and need to be scanned over a greater range (e.g. all applications).

The algorithm of the present invention has the effect of nearly doubling the number of codewords that can be corrected in matrix symbology decodes, thereby greatly improving the performance over what is currently available.

The foregoing illustrative summary, as well as other exemplary objectives and/or advantages of the invention, and the manner in which the same are accomplished, are further explained within the following detailed description and its accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of an exemplary hand-held symbol reader acquiring data from a machine-readable symbol.

FIG. 2 is an internal block diagram of an exemplary symbol reader for acquiring data from a machine-readable symbol

FIG. 3 illustrates several exemplary machine-readable 2D symbols.

FIG. 4 provides two views of an exemplary 2D symbol which is damaged.

FIG. 5 is a flow-chart of an exemplary method for optically enhanced Reed-Solomon error-correction for a 2D symbol.

FIG. 6 is a flow-chart of an exemplary method for contrast analysis for a 2D symbol as part of enhanced Reed-Solomon error correction.

FIG. 7 presents an exemplary array of codeword contrast values used for enhanced error correction by applying contrast analysis to a flawed codeword.

FIG. 8 illustrates an exemplary case-study of enhanced error correction by applying contrast analysis to a flawed codeword.

DETAILED DESCRIPTION

In the following description, certain specific details are set forth in order to provide a thorough understanding of various embodiments. However, one skilled in the art will understand that the invention may be practiced without these details. In other instances, well-known structures associated with imagers, scanners, and/or other devices operable to read machine-readable symbols have not been shown or described in detail to avoid unnecessarily obscuring descriptions of the embodiments.

Unless the context requires otherwise, throughout the specification and claims which follow, the word “comprise” and variations thereof, such as, “comprises” and “comprising” are to be construed in an open sense, that is as “including, but not limited to.”

Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

The headings provided herein are for convenience only and do not interpret the scope or meaning of the claimed invention.

Symbol Reader

The present system and method embraces devices designed to read machine-readable symbols.

In an exemplary embodiment, such a device may be a hand-held scanner. FIG. 1 is a perspective view of an exemplary hand-held symbol reader 100 acquiring data from a machine-readable symbol 102.

The machine-readable symbol 102 is affixed to a package 104 or the like such that the user points the hand-held symbol reader 100 towards the machine-readable symbol 102. The symbol reader 100 may be a line scanner operable to emit and sweep a narrow beam of electromagnetic energy across a field-of-view 106 over two-dimensional (2D) machine-readable symbol 102. In other embodiments, an aperture means, mirror, lens or the like is adjusted to sweep across a symbol line to receive returning electromagnetic energy from a relatively small portion (e.g., cell) of the machine-readable symbol, which is detected by an optical detector system.

In yet other embodiments, a 2D array symbol reader acquires a captured image of the machine-readable symbol (and a suitable region of quiet area around the machine-readable symbol). For the present system and method, which relies upon a contrast analysis of the cells within the symbol 102, the acquisition of a captured image of the symbol may be a preferred method of operation for the symbol reader 100. Suitable image processing hardware 235 and software running on processors 242, 244 are used to deconstruct the capture image to determine the data bits represented by the cells, and to perform the contrast analysis of the present system and method (see FIG. 2 below).

The machine-readable symbol reader 100 is illustrated as having a housing 108, a display 110, a keypad 112, and an actuator device 114. Actuator device 114 may be a trigger, button, or other suitable actuator operable by the user to initiate the symbol reading process.

The machine-readable symbol 102 shown in the figure is intended to be generic and, thus, is illustrative of the various types and formats of machine-readable symbols. For example, some machine-readable symbols may consist of a single row of codewords (e.g., barcode). Other types of machine-readable symbols (e.g., matrix or area code) may be configured in other shapes, such as circles, hexagons, rectangles, squares and the like. It is intended that many various types and formats of machine-readable symbologies be included within the scope of the present system and method.

Symbol Reader Internal Block Diagram

An internal block diagram of an exemplary symbol reader 100 of a type which may implement the present system and method is shown in FIG. 2.

In one embodiment of the present system and method, the symbol reader 100 may be an optical reader. Optical reader 100 may include an illumination assembly 220 for illuminating a target object T, such as a 1D or 2D bar code symbol 102, and an imaging assembly 230 for receiving an image of object T and generating an electrical output signal indicative of the data which is optically encoded therein. Illumination assembly 220 may, for example, include an illumination source assembly 222, such as one or more LEDs, together with an illuminating optics assembly 224, such as one or more reflectors, for directing light from light source 222 in the direction of target object T. Illumination assembly 220 may be eliminated if ambient light levels are certain to be high enough to allow high quality images of object T to be taken.

In an embodiment, imaging assembly 230 may include an image sensor 232, such as a 2D CCD or CMOS solid state image sensor, together with an imaging optics assembly 234 for receiving and focusing an image of object T onto image sensor 32. The array-based imaging assembly shown in FIG. 2 may be replaced by a laser scanning based imaging assembly comprising a laser source, a scanning mechanism, emit and receive optics, a photodetector and accompanying signal processing circuitry. The field of view of the imaging assembly 230 will depend on the application. In general, the field of view should be large enough so that the imaging assembly can capture a bit map representation of a scene including an image data reading region at close reading range.

In an embodiment of the present system and method, exemplary symbol reader 100 of FIG. 2 also includes programmable controller 240 which may comprise an integrated circuit microprocessor 242 and an application specific integrated circuit (ASIC) 244. Processor 242 and ASIC 244 are both programmable control devices which are able to receive, output and process data in accordance with a stored program stored in either or both of a read/write random access memory (RAM) 245 and an erasable read only memory (EROM) 246. Processor 242 and ASIC 244 are also both connected to a common bus 248 through which program data and working data, including address data, may be received and transmitted in either direction to any circuitry that is also connected thereto. Processor 242 and ASIC 244 may differ from one another, however, in how they are made and how they are used.

In one embodiment, processor 242 may be a general purpose, off-the-shelf VLSI integrated circuit microprocessor which has overall control of the circuitry of FIG. 2, but which devotes most of its time to decoding image data stored in RAM 245 in accordance with program data stored in EROM 246. Processor 244, on the other hand, may be a special purpose VLSI integrated circuit, such as a programmable logic or gate array, which is programmed to devote its time to functions other than decoding image data, and thereby relieve processor 242 from the burden of performing these functions.

In an alternative embodiment, special purpose processor 244 may be eliminated entirely if general purpose processor 242 is fast enough and powerful enough to perform all of the functions contemplated by the present system and method. It will, therefore, be understood that neither the number of processors used, nor the division of labor there between, is of any fundamental significance for purposes of the present system and method.

In an embodiment, exemplary symbol reader 100 includes a signal processor 235 and an analog-to-digital (A/D) chip 236. These chips together take the raw data from image sensor 232 and convert the data to digital format, which in an exemplary embodiment may be a gray-level digital format, for further processing by programmable controller 240.

In an embodiment, the system and method of the present invention employs algorithms stored in EROM 246 which enable the programmable controller 240 to analyze the image data from signal processor 235 and A/D 236. In an embodiment, and as described further below, this image analysis may include analyzing gray-level information (contrast levels) in the image data. In an embodiment, and in part based on the contrast level analysis, programmable controller 240 may then implement an improved system and method of error correction for matrix symbols by relying on optical contrast-level analysis, as also described further below.

Exemplary symbol reader 100 may also include input/output (I/O) circuitry 237, for example to support the use of the keyboard 112 and trigger 114. Symbol reader 100 may also include output/display circuitry 238 to support display 110.

Exemplary Symbols

FIG. 3 illustrates several exemplary machine-readable 2D symbols 102 labeled 102.1 and 102.2.

Symbol 102.1 is an exemplary machine-readable symbol encoded according to the Data Matrix barcode (ECC 200) standard. The symbol 102.1, which is a 24×24 array, has two solid black borders 302 forming an “L-shape” which are the finder pattern, enabling the symbol reader to determine the location and orientation of the 2D symbol. The symbol also has two opposing borders of alternating dark and light cells which form a “timing pattern” 304 which help the symbol reader identify the size (the number of rows and columns) of the symbol.

Interior to the finder pattern 302 and timing pattern 304 are rows and columns of interior cells 306 which encode information. As may be evident from the figure, an ideal machine-readable symbol has a very high contrast level between the first color dark cells and the second color light cells, in many cases achieved by employing clearly printed, unobscured cells which are either all black or all white.

Symbol 102.2 is an exemplary 16×16 machine-readable symbol encoded according to the Data Matrix barcode (ECC 200) standard. In symbol 102.2, and for purposes of illustration only, the interior black data cells are omitted, and boundaries between the interior cells 306 are suggested by shaded, dotted lines which are not normally present in actual printed data matrix symbols.

Also not normally present in actual printed symbols, but included here for purposes of illustration, are solid borders which indicate the boundaries of the codewords 308 formed by the interior cells 306. In an embodiment, each codeword 308 is composed of eight cells representing a single byte of data. It will be seen that there are several types of codewords, including data codewords 308.1 which encode the actual data to be represented by the symbol; error-correcting (EC) codewords 308.2 which are generated from the data codewords according to the Reed-Solomon algorithm; and padding codewords 308.3.

The figure also identifies one exemplary bar (black) cell 306.B and one exemplary space (white) cell 306.S.

The illustration here of machine-readable symbols based on the Data Matrix barcode standard, as well as the size, shape, and data contents illustrated, are exemplary only and should not be construed as limiting. The present system and method is applicable to a wide variety of 2D matrix barcodes according to a variety of known standards, as well as being applicable to other 2D machine-readable symbols which may be envisioned in the future.

Symbol Errors

As discussed above, the data content of symbols 102 is stored or presented in the form of cells 306 of contrasting colors within codewords 308. In an embodiment of the present system and method, the light cells (typically white) represent ones (1's) and the dark cells (typically black) represent zeros (0's). In an alternative embodiment, a light cell represents zero (0) and the dark cells represent (1). In alternative embodiments, other colors or levels of shading may be employed. As a general matter, however, for the coding to be effective the symbol reader 100 must be readily able to distinguish the dark cells from the light cells. Also, the data is stored not only in terms of the cells 306 per se, but also in terms of the positions of the cells 306 within the codewords 308, and the positions of each codeword 308 within the symbol 102.

If a symbol 102 is damaged, there may be insufficient contrast between light cells and dark cells for the symbol reader 100 to reliable distinguish the cells. Similarly, damage to the symbol may render it difficult for the symbol reader to identify the location or boundaries of cells 306 and codewords 308. In other cases damage to cells 306 can cause a change from black to white or vice-versa. This in turn calls upon the error-correction methods, such as Reed-Solomon, already discussed above. The present system and method is intended to augment Reed-Solomon and similar error-correction methods with information based on contrast analysis.

FIG. 4 provides two views 102.D1, 102.D2 of an exemplary symbol 102.D which is damaged, so that the original high-contrast has been lost while the symbol 102 is in use in the field.

In the first view, the damaged symbol 102.D1 shown in the figure was photographed in a real-world automotive manufacturing plant. It is apparent that there is a dark vertical scuff mark 402 which is approximately down the middle of the symbol 102.D1. The scuffing is sufficiently dark that, when read with a standard symbol reader 100, the reader 100 mistakes many individual cells 306 for black when (as printed, and without damage or scuffing) they are white cells. This in turns causes codeword errors. This symbol 102.D1 will not read with current scanners.

The actual value of the codewords in symbol 102.D1 is listed here (codewords before the colon are data codewords, those after the colon are error-correction codewords):

237 151 230 204 27 207 144 165 112 27 13 43 222 60 125 34 137 186 71 163 223 254:96 9 171 31 209 21 131 100 111 146 225 95 109 112 182 218 118 203

The values for the codewords determined by a symbol reader 100 are shown here, with the incorrect codewords underlined:

237 151 230 204 27 207 144 165 112 27 173 111 222 60 125 34 137 191 127 235 223 254:96 25 175 191 208 21 131 100 111 146 225 95 111 116 182 218 118 203

As is apparent in the image of symbol 102.D1, throughout the smudged region 402 the contrast between many individual cells is small, and is close to the threshold level between black and white. Compare for example a cluster of low contrast cells 404 within the smudged region 402 with a non-damaged, machine-readable high contrast region 406.

In the second view, the damaged symbol 102.D2 is illustrated as it was interpreted by an actual scanner 100 in the field. As shown by the codewords with shaded cells 306 in the illustration, there were eleven codewords 308 which provided flawed readings from the scanner 100, and may be described as flawed codewords 308.F.

Erasure Vs. Error:

By way of terminology, it is noted here that if the position of an erroneous codeword is known, but the data is not known (or is ambiguous), the codeword is referred to as an “erasure.” If the data of an erroneous codeword is unknown and the position of the codeword is also unknown, the codeword is referred to as an “error.”

Reed-Solomon Error Correction

In an embodiment, the present system and method includes application of error-correcting codes and analyses, augmented with optical analysis of a machine-readable symbol 102, to detect and correct errors in the machine-readable symbol 102. Various mathematical methods of error correction are well-known in the art, and a detailed description is beyond the scope of this document. However, review of a few basic elements of an exemplary error-correction method may aid in the understanding of the present system and method.

All standardized 2D matrix symbologies utilize the Reed-Solomon methodology. In Reed-Solomon codes, a set of data elements, such as bytes of data, may be redundantly encoded in a second set of error-correcting elements (also typically in byte form), which for present purposes can be referred to as EC codewords 308.2. The error-correcting codewords are transmitted or presented along with the principle data elements, enabling reconstruction of damaged data elements.

Methods of constructing the Reed-Solomon EC codewords (based on a given, particular data set) are outside the scope of this document. It suffices for present purposes to understand that Reed-Solomon-derived EC codewords 308.2 can be calculated, and the resulting EC codewords are included as part of 2D matrix symbols, as already described above.

There are a variety of methods of decoding a message with Reed-Solomon error correction. In one exemplary method, the values of the data codewords 308.1 of a symbol 102 are viewed as the coefficients of a polynomial s(x) that is subject to certain constraints (not discussed here):

${S(x)} = {\sum\limits_{i = 0}^{n - 1}{c_{i}x^{i}}}$

It will be noted that not only the values of the data codewords 308.1 matter, but also their order. The ordinal placement of the codewords (1^(st), 2^(nd), 3^(rd), etc.) in the polynomial maps to the physical ordering of the data codewords 308.1 in the machine-readable symbol 102.

If the machine-readable symbol 102 is damaged or corrupted, this may result in data codewords 308.1 which are incorrect. The erroneous data can be understood as a received polynomial r(x):

r(x) = s(x) + e(x) ${e(x)} = {\sum\limits_{i = 0}^{n - 1}{e_{i}\mspace{11mu} x^{i}}}$

where e_(i) is the coefficient for the i^(th) power of x. Coefficient e_(i) will be zero if there is no error at that power of x (and so no error for the corresponding i^(th) data codeword 308.1 in the symbol 102); while the coefficient e_(i) will be nonzero if there is an error. If there are ν errors at distinct powers i_(k) of x, then:

${e(x)} = {\sum\limits_{k = 1}^{N}{\left( {e\_ i}_{k} \right)\; \left( {x^{\bigwedge}i_{k}} \right)}}$

The goal of the decoder is to find the number of errors (ν), the positions of the errors (i_(k)), and the error values at those positions (e_i_(k)). From those, e(x) can be calculated, and then e(x) can be subtracted from the received r(x) to get the original message s(x).

There are various algorithms which can be employed, as part of the Reed-Solomon scheme, to identify the error positions (i_(k)) and the error values at those positions (e_i_(k)), based solely on the received data codewords 308.1 and the received EC codewords 308.2. The processes involved, however, are generally a two-stage processes, where:

Stage (I) Error Locations:

The first calculation stage entails identifying the location of the errors. This entails first calculating an error-locator polynomial Λ, and based on Λ, calculating the non-zero error positions i_(k). This stage also determines the number of errors (ν). This first stage calculation inevitably requires the use of some of the EC codewords 308.2 in the symbol 102.

Stage (II) Corrected Values:

Employing the location errors i_(k) as calculated in stage (i), the second calculation stage identifies the correct values (e_i_(k)) associated with each error location.

It will be seen then that in the prior art, correcting errors is a two-stage process, where identifying error locations generally precedes, and is an input to, identifying the corrected data at each location. It is a goal of the present system and method to either reduce or possibly eliminate the calculations of stage (I), by using analyses apart from Reed-Solomon error correction to determine identify or mark the erroneous data codewords 308.1.

Persons skilled in the art will recognize that the non-zero error positions i_(k) calculated via the alternative methods (discussed further below) can be input directly into stage (II), thereby enabling the calculations of the correct data values in stage (II).

Importantly, in the mathematics of standard Reed-Solomon error correction, errors (both location and data unknown) requires the use of two error correcting code words to repair a damaged codeword. If, on the other hand, knowledge of the location of the error exists, then the error is considered an erasure, and only one error correction codeword is required to repair the erased codeword.

Stated another way: Normally, error-correction in 2D matrix symbologies is used to correct codewords which are errors, meaning that both the location and contents of the codeword are unknown. The goal of the present system and method is to independently flag errors so that they are instead treated as erasures, for which the location is known, thereby requiring only one EC codeword for correction.

Optical Clarity and Optical Ambiguity, Decoding Disadvantage, and Reed-Solomon Error Correction

As discussed above, Reed-Solomon error correction requires the use of two EC codewords 308.2 to correctly recover both the location and the data contents of a single data codeword 308.1 which is flawed. However, the present system and method aims to enable the identification (at least provisionally) of the locations of the flawed or damaged codewords 308.F—and to make such identification independently of the EC codewords 308.2 in the symbol 102. Such alternative means of locating the data codewords 308.1 which are flawed supplements the data in the EC codewords 308.2; as a result, only a single EC codeword 308.2 is required to identify the data in a data codeword 308.1 Flawed codewords 308.F may also be referred to as codewords which have a “decoding disadvantage.”

To identify the locations of the codewords with a decoding disadvantage, independent of the error-correcting information within the symbol 102 itself, the present system and method identifies those codewords 308 in the symbol 102 which have a low level of optical clarity, or equivalently, a high level of optical ambiguity. By “optical clarity” is meant any codeword 308 which, as presented to the reader 100, is sufficiently clear and distinct (e.g., has high optical contrast) to be read very reliably by the symbol reader's optical system 230, 235. If a codeword 308 is not optically clear—for example, due to poor printing, smudging or marking in the field, ripping or tearing, or other causes—then the codeword is deemed optically ambiguous; there is a significant probability that the data for an optically ambiguous codeword, as determined by a reader 100, will not match the intended data of the same codeword.

FIG. 5 presents a flow-chart of an exemplary method 500 for optically enhanced Reed-Solomon error-correction for a symbol 102. The steps of exemplary method 500 are generally performed via the processor(s) 240, memory 245, and other components of the symbol reader 100.

In step 505, the symbol reader 100 identifies the location of the symbol 102 and the appropriate parameters such as the size. For example, for a DataMatrix symbol, the reader 100 finds the “L-shape” 302 and finds the clock track 304 to identify the number of rows and columns in the symbol. The L-shape 302 and clock track 304 help the reader 100 determine the symbol's tilt and orientation, and provide reference points from which to decode the matrix of data cells.

In step 510, the symbol reader 100 creates a matrix or array of sample points (pixels), indicating the reflectances (bright or dark) of points within the symbol 102. These sample points are used to determine reflectance of cells 306 within the symbol. A single cell 306 may have multiple sample points measured, and together these may be used (for example, averaged) to determine the reflectance of each cell 306.

As discussed above, the symbol 102 is composed of codewords 308 with standardized positions, that is, which are made up of standardized clusters of cells 306 with designated positions within the symbol matrix 102.

In step 515, the method 500 determines a level of optical clarity for each codeword 308. A high level of optical clarity, which is desirable, means the codeword's cells are distinctive and that the data value of the codeword can be read with a high probability of accuracy.

A low level of optical clarity—or equivalently, a high level of optical ambiguity—may result from physical damage to a symbol, or from dirt or grease marking the symbol, or other causes as discussed above. Low optical clarity, or high optical ambiguity, means that the codeword's cells are not distinctive and the codeword has a decoding disadvantage. The low level of optical clarity therefore means that the data value of the codeword can be ascertained only with a suboptimal degree of reliability.

Optical clarity/ambiguity may be determined in a variety of ways. In one embodiment of the present system and method, discussed in detail below, the optical clarity/ambiguity is determined based on an analysis of the contrast level between cells 306 within each codeword 308. Codewords 306 which exhibit the lowest internal contrast levels may be marked as optically ambiguous.

In an alternative embodiment, optical clarity/ambiguity may be determined based on analysis of the degree to which a codeword 308 is in-focus or not in-focus. In an alternative embodiment, optical clarity/ambiguity may be determined based on analysis of the definition or lack of definition of lines separating the dark cells 306 from light cells 306.

In an alternative embodiment, optical clarity/ambiguity may be determined based on a degree to which the horizontal and vertical lines of the codewords 308 are parallel to, or are not parallel to, the border-L shape. Other methods of assessing optical clarity of a codeword 308 may be envisioned as well, and fall within the scope and spirit of the present system and method.

In step 520, exemplary method 500 ranks the codewords 308 according to optical clarity, for example from highest to lowest in optical clarity. In step 525, method 500 identifies the lowest ranked codewords (those which are most optically ambiguous), up to the number of codewords 308 to be used as erasures.

In steps 530 and 535, the lowest-ranked codewords 308 identified in step 525—that is, the codewords with the highest optical ambiguity—are marked as erasures in the error-correction equations, and the Reed-Solomon error-correction equations are then executed. Steps 530 and 535 thereby reduce or eliminate the calculations discussed above for a phase (I) of the Reed-Solomon error correction process, and thereby also reduce or eliminate the use of EC codewords 308.2 to identify the locations of flawed codewords 308.F.

Gray-Scale Contrast Analysis Algorithm

In one embodiment, the present system and method identifies codewords 308 with high optical ambiguity (low optical clarity) via contrast analysis of the codewords within the symbol 102.

The present system and method employs a “matrix-cell contrast analysis algorithm,” “gray-scale contrast analysis algorithm,” or simply “contrast analysis algorithm” (CAA) for short. The contrast analysis algorithm of the present system and method determines the actual gray level of each cell 306 in the symbol 102. The CAA also identifies the black/white contrast threshold for the symbol 102. The black/white contrast threshold is the brightness level above which a cell 306 is considered to be white, and below which a cell is considered to be black. The algorithm then determines the difference between the contrast level of each cell 306 and the black/white threshold. If the differential is comparatively low for one or more cells 306 in a particular codeword 308, the codeword 306 may have a decoding disadvantage.

More generally, the CAA may identify a light/dark threshold level, which is a brightness level above which a cell 306 is considered to be of a first, lighter color (for example, white); and below which a cell is considered to be of a second, darker color (for example, black).

A scanner 100 will conventionally store, in memory 245, the “color” of each cell 306, for example, a red-green-blue (RGB) value or a hue-saturation-brightness (HSB) value. The present system and method will also store, in the memory (245) of the scanner 100, an actual, measured gray-scale level for each cell 306.

FIG. 6 presents a flow-chart of an exemplary method 600 for contrast analysis according to the present system and method. Steps 605 through 645 of exemplary method 600 collectively may be considered to be one exemplary embodiments of step 515 of method 500, already discussed above. (Step 515 determines an optical clarity for each codeword 308 in the symbol 102.) Step 650 of exemplary method 600 may be considered to be one exemplary embodiment of step 520 of method 500, that is, ranking the codewords for optical clarity.

Where exemplary method 500 was directed to generally determining and ranking codewords 308 by optical clarity, the exemplary method 600 particularly employs an exemplary approach to contrast analysis in order to determine and rank optical clarity. The steps of exemplary method 600 are generally performed via the processor(s) 240, memory 245, and other components of the symbol reader 100.

In step 605, the symbol reader 100 determines a local black/white contrast threshold (BWCT). The black/white contrast threshold (BWCT), as described above, is a reflectance level above which a cell 306 is considered white, and below which a cell 306 is considered black. This is typically determined by (i) identifying the reflectance of all the cells 306 in the symbol; (ii) identifying the highest reflectance value and the lowest reflectance value; and (iii) identifying a middle-value, such as the mean or the median, and using the middle-value as the BWCT. The present system and method refines this by employing a local BWCT for each cell 306. In an exemplary embodiment, a local BWCT for a given cell 306 may be determined by considering only those other cells local to the given cell 306, and then identifying the mean or median reflectance among those cells. In an embodiment, the number of local cells used to determine the local BWCT may be twenty (20). In an alternative embodiment the number of local cells used to determine the BWCT for a given cell may be higher or lower than twenty (20).

In step 610, the method 600 selects a particular codeword 308, (as specified in the appropriate standards for the size and shape of the symbol 102), and identifies the contrast level (the grayscale level) of each cell in the codeword.

In step 615, the method 600 determines, for the particular codeword at hand, a bar cell (306.B) with a contrast value closest to the BWCT; and a space cell (306.S) with a contrast value closest to the BWCT; and then stores these two cell contrast values in a codeword contrast values array in memory (see FIG. 7 below for an example). The contrast values may be labeled as RSmin for the space cell (306.S) closest to the BWCT, and RBmax for the bar cell (306.B) closest to the BWCT. An equivalent phrasing: RSmin is the smallest space cell reflectance (darkest), and RBmax is the largest bar cell reflectance (lightest).

Steps 610 and 615 are repeated for all codewords 308 in the symbol 102. This results in a listing of RSmin and RBmax for each codeword 308 in the symbol.

In step 620, the method 600 determines the erasure gap for spaces between RSmin and the local black/white contrast threshold for each codeword. (ESgap=RSmin−localBWCT)

In step 625, the method 600 determines the erasure gap for bars between RBmax and the local black/white contrast threshold for each codeword. (EBgap=localBWCT−RBmax)

In step 630, the method 600 identifies the largest space cell value in the entire array, that is the largest value for RSmin. This value, which may be labeled as RSmm, is used for normalization in the following step.

In step 635, the method 600 divides all space gap value entries (ESgap) by the largest space cell (“white cell”) value in the array, RSmm, generating an Sgap % value for each codeword. (Sgap %=ESgap/RSmm)

In step 640, the method 600 identifies the largest bar cell (“black cell”) value in the entire array, that is the largest value for RBmin. This value, which may be labeled as RBmm, is used for normalization in the following step.

In step 645, the method 600 divides all bar gap value entries (EBgap) by the largest bar cell value in the array, RBmm, generating a Bgap % value for each codeword. (Bgap %=EBgap/RBmm)

Sgap % and Bgap %, then, are the percentage relative closeness of the deviant cell to the black/white contrast threshold. These percentage values, Sgap % and Bgap %, may also be referred to as the minimum interior contrast levels 702 for each cell 306. The minimum interior contrast levels 702 are a measure of the optical clarity of the codewords 308 in the symbol 102. Specifically: Those codewords 308 with the lowest values for Sgap % and/or the lowest values for Bgap % have the highest optical ambiguity (and therefore the least or worst optical clarity).

As noted above, the preceding steps 605 through 645 of method 600 may collectively be considered to be one exemplary embodiment of step 515 of method 500, already discussed above, that is, determining an optical clarity for each codeword 308 in the symbol 102.

In step 650, and based on the Sgap % and Bgap % values determined in steps 635 and 645, the method 600 ranks the lowest gap percent values up to the number of error correction codewords to be used as erasures. Step 650 of exemplary method 600 may be considered to be one exemplary embodiment of step 520 of method 500, that is, ranking the codewords for optical clarity/ambiguity.

These lowest ranked, least clear codewords are the codewords with the lowest optical clarity (or highest ambiguity), which are then used as erasures in the Reed-Solomon equations (step 530 of method 500).

Sample Applications

FIG. 7 presents an exemplary codeword contrast values array 700 of the kind which may be constructed according to exemplary method 600, above. The array contains actual codeword measurements for the symbol image 102.D1/102.D2 of FIG. 4, above. In array 700, CW is the codeword number; and, as per discussion above:

-   -   RSmin is the smallest (darkest) space cell reflectance for each         codeword 308;     -   RBmax is the largest (lightest) bar cell reflectance for each         codeword 308;     -   ESgap is the erasure space gap calculated as RSmin minus the         threshold (75 hex in this case);     -   EBgap is the threshold minus RBmax for the bar cells;     -   Sgap % and Bgap % are the relative closeness of the deviant cell         to the black/white threshold in percent, also referred to as the         minimum interior contrast levels 702; and     -   Rank is a listing of the worst 12 codewords (those with the         smallest gap percentage) in the symbol 102.

FIG. 8 illustrates an exemplary case-analysis demonstrating how poor cell contrast can identify a majority of flawed codewords 308.F. The damaged symbols shown in the figure are the same as the damaged symbol pictured and illustrated in FIG. 4, above. In FIG. 8, numbered codeword locations 805 are identified (by a standardized number scheme) for those codewords which are flowed or damaged.

102.D2, reproduced here from FIG. 4 for convenience, is the damaged symbol as it was interpreted by an actual scanner 100 in the field.

Symbol 102.D3 is the same symbol as it was interpreted according the exemplary contrast analysis algorithms discussed above in conjunction with FIG. 5 and FIG. 6.

As can be seen in FIG. 8, there are two codewords 815 which were assessed as being in error by the present system and method, but which were actually read correctly by the scanner 100. Of the latter codewords, one was in the damaged region 402 (codeword 27) and another was a codeword where there is a scratch through the dark cell, making it lighter (codeword 22).

As can also be seen from FIG. 8, there is one codeword 810 which was actually read in error by the scanner 100, but was not flagged by the gray-scale contrast analysis algorithm of the present system and method.

All the remaining, identified codewords 308 (a total of ten) which were flagged as being in error based on contrast analysis are codewords which were, in fact, read in error by the scanner 100.

The codeword that the analysis missed (codeword 27) is easily decoded using the 6 error correction codewords still remaining. This is an example of a symbol 102.D that was far from being decodable using standard decoding methods, yet using a gray-scale contrast analysis algorithm, the symbol can sustain this and slightly more damage and still be decodable.

Further Applications

The example shown (in FIGS. 4 and 8) clearly benefits from the gray-scale contrast analysis decoding since the damage to the symbol 102.D1/102.D2 is contrast based. However, the present system and method will also work with other types of damage such as matrix distortion, uniform dark or light damage and for DPM cell variation. When these types of distortion are present, there will be many sample points that rest on cell boundaries which will be recorded as reduced contrast values. As long as the matrix distortion (such as wrinkling) is localized or the dark/light damage is less than approximately one-third of the symbol, the present system and method will substantially improve decoding rates on all types of problem symbols 102.D.

SUMMARY

Improved matrix symbology decode performance is possible when there is some knowledge of potentially damaged codewords 308. One means of achieving improved decode performance is by measuring the gray-level contrast variation of every codeword, and marking those with contrast values that are closest to the black/white threshold as erasures. Using gray-level information and using erasure correction in matrix symbologies will allow successful decoding far into a damage region where current product decoding fails.

To supplement the present disclosure, this application incorporates entirely by reference the following patents, patent application publications, and patent applications:

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In the specification and/or figures, typical embodiments of the invention have been disclosed. The present invention is not limited to such exemplary embodiments. The use of the term “and/or” includes any and all combinations of one or more of the associated listed items. The figures are schematic representations and so are not necessarily drawn to scale. Unless otherwise noted, specific terms have been used in a generic and descriptive sense and not for purposes of limitation.

The foregoing detailed description has set forth various embodiments of the devices and/or processes via the use of block diagrams, flow charts, schematics, exemplary data structures, and examples. Insofar as such block diagrams, flow charts, schematics, exemplary data structures, and examples contain one or more functions and/or operations, it will be understood by those skilled in the art that each function and/or operation within such block diagrams, flowcharts, schematics, exemplary data structures, or examples can be implemented, individually and/or collectively, by a wide range of hardware, software, firmware, or virtually any combination thereof.

In one embodiment, the present subject matter may be implemented via Application Specific Integrated Circuits (ASICs). However, those skilled in the art will recognize that the embodiments disclosed herein, in whole or in part, can be equivalently implemented in standard integrated circuits, as one or more computer programs running on one or more computers (e.g., as one or more programs running on one or more computer systems), as one or more programs running on one or more controllers (e.g., microcontrollers) as one or more programs running on one or more processors (e.g., microprocessors), as firmware, or as virtually any combination thereof, and that designing the circuitry and/or writing the code for the software and or firmware would be well within the skill of one of ordinary skill in the art in light of this disclosure.

In addition, those skilled in the art will appreciate that the control mechanisms taught herein are capable of being distributed as a program product in a variety of tangible forms, and that an illustrative embodiment applies equally regardless of the particular type of tangible instruction bearing media used to actually carry out the distribution. Examples of tangible instruction bearing media include, but are not limited to, the following: recordable type media such as floppy disks, hard disk drives, CD ROMs, digital tape, flash drives, and computer memory.

The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the present systems and methods in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the invention to the specific embodiments disclosed in the specification and the claims, but should be construed to include all machine-readable symbol scanning and processing systems and methods that read in accordance with the claims. Accordingly, the invention is not limited by the disclosure, but instead its scope is to be determined entirely by the following claims. 

What is claimed is:
 1. A method of error correction for a two-dimensional (2D) symbol designed for optical reading by a symbol reader, the 2D symbol having a plurality of cells of a designated first color and a designated second color which cells are arranged in a two-dimensional matrix; the 2D symbol further having a plurality of codewords at specified locations within the symbol, each codeword comprising at least one specified group of cells; the plurality of codewords comprising a first plurality of codewords storing data indicated by the pattern of first and second color cells in the codeword, and a second plurality of error-correction (EC) codewords derived from the data codewords and providing redundancy for the data represented by the data codewords, the method comprising: optically reading, by an optical scanner of the symbol reader, the plurality of codewords in the symbol; determining, via a hardware processor of the symbol reader, a location for a codeword which is optically ambiguous; marking via the hardware processor, in an error correction (EC) equation stored in a memory of the symbol reader, the location of the optically ambiguous codeword within the symbol; and executing, via the hardware processor, the EC equation to correct errors in the read plurality of codewords.
 2. The method of claim 1, wherein determining the location for the codeword which is optically ambiguous comprises: determining a location for a codeword which displays a level of contrast between the first color and the second color which is insufficient for an unambiguous decoding of the codeword by the symbol reader.
 3. The method of claim 1, wherein determining a location for a codeword which is optically ambiguous comprises: selecting a codeword location based on a standards-established set of codeword locations within the symbol; and performing a contrast analysis on the codeword at the selected location, wherein the contrast analysis identifies a minimum interior contrast level for the selected codeword.
 4. The method of claim 3, further comprising: identifying a respective minimum interior contrast level for each codeword in the symbol; and flagging as optically ambiguous a plurality of codewords with the lowest minimum interior contrast levels among all the codewords in the symbol, up to a specified number of codewords.
 5. The method of claim 3, wherein performing the contrast analysis on the codeword comprises: (i) determining a dark/light threshold level, wherein the dark/light threshold level is indicative of a reflectance above which a cell is assessed as being of the first color and below which a cell is assessed as being of the second color; (ii) determining a level of difference between the reflectance of each cell of the codeword and the dark/light threshold level; and (iii) determining the minimum interior contrast level for the codeword by determining, among all the cells within the codeword, a specific cell with a lowest level of difference between the reflectance of the specific cell and the dark/light threshold level.
 6. The method of claim 5, further comprising: ranking each codeword of the symbol for a respective level of optical ambiguity, wherein each codeword is ranked for its respective level of optical ambiguity based on the minimum interior contrast level of that codeword as compared with the minimum interior contrast levels of all the other codewords in the symbol, wherein: a first minimum interior contrast level of a first codeword is compared with a second minimum interior contrast level of a second codeword, the codeword of the two with the lower minimum interior contrast level being assigned a higher level of optical ambiguity.
 7. The method of claim 5, further comprising: (i) determining a local dark/light threshold level for a specific cell, wherein the local dark/light threshold level for the specific cell is determined based on a plurality of cells local to the specific cell; (ii) determining a level of difference between the reflectance of each cell of the codeword and each cell's local dark/light threshold level; and (iii) determining the minimum interior contrast level for the codeword by determining, among all the cells within the codeword, a specific cell with a lowest level of difference between the reflectance of the specific cell and the cell's local dark/light threshold level.
 8. An electronic system that acquires a machine-readable two-dimensional (2D) symbol designed for optical reading by the system, the 2D symbol having a plurality of cells of a designated first color and a designated second color which cells are arranged in a two-dimensional matrix; the 2D symbol further having a plurality of codewords at specified locations within the symbol, each codeword comprising at least one specified group of cells; the plurality of codewords comprising a first plurality of codewords storing data indicated by the pattern of first and second color cells in the codeword, and a second plurality of error-correction (EC) codewords derived from the data codewords and providing redundancy for the data represented by the data codewords, the electronic system comprising: an optical scanner configured to optically receive the plurality of cells in the symbol and to convert the cell pattern of the symbol into an electrical pattern subject to electronic storage and computational analysis; a memory configured to store the electrical pattern of the symbol, and an error-correction (EC) equation; and a hardware processor which is configured to: determine a location for a codeword which is optically ambiguous; mark in the error correction equation the location of the optically ambiguous codeword within the symbol; and execute the EC equation to correct errors in the read plurality of codewords.
 9. The electronic system of claim 8, wherein the hardware processor is further configured to determine a location for a codeword which is optically ambiguous by: determining a location for a codeword which displays a level of contrast between the first color and the second color which is insufficient for an unambiguous decoding of the codeword by the electronic system.
 10. The electronic system of claim 8, wherein the hardware processor is further configured to determine the location for a codeword which is optically ambiguous by: selecting a codeword location based on a standards-established set of codeword locations within the symbol, said standards-established set being stored in the memory of the electronic system; and performing a contrast analysis on the codeword at the selected location, wherein the contrast analysis identifies a minimum interior contrast level for the selected codeword.
 11. The electronic system of claim 10, wherein the hardware processor is further configured to: identify a respective minimum interior contrast level for each codeword in the symbol; and flag as optically ambiguous a plurality of codewords with the lowest minimum interior contrast levels among all the codewords in the symbol, up to a specified number of codewords.
 12. The electronic system of claim 10, wherein to perform the contrast analysis on the codeword the hardware processor is further configured to: (i) determine a dark/light threshold level, wherein the dark/light threshold level is indicative of a reflectance above which a cell is assessed as being of the first color and below which a cell is assessed as being of the second color; (ii) determine a level of difference between the reflectance of each cell of the codeword and the dark/light threshold level; and (iii) determine the minimum interior contrast level for the codeword by determining, among all the cells within the codeword, a specific cell with a lowest level of difference between the reflectance of the specific cell and the dark/light threshold level.
 13. The electronic system of claim 12, wherein the hardware processor is further configured to: rank each codeword of the symbol for a level of optical ambiguity, wherein each codeword of the symbol is ranked for the level of optical ambiguity based on the minimum interior contrast level of that codeword as compared with the minimum interior contrast levels of all the other codewords in the symbol, wherein: a first minimum interior contrast level of a first codeword is compared with a second minimum interior contrast level of a second codeword, the codeword of the two with the lower minimum interior contrast level being assigned a higher level of optical ambiguity.
 14. The electronic system of claim 12, wherein the hardware processor is further configured to: (i) determine a local dark/light threshold level for a specific cell, wherein the local dark/light threshold level for the specific cell is determined based on a plurality of cells local to the specific cell; (ii) determine a level of difference between the reflectance of each cell of the codeword and each cell's local dark/light threshold level; and (iii) determine the minimum interior contrast level for the codeword by determining, among all the cells within the codeword, a specific cell with a lowest level of difference between the reflectance of the specific cell and the cell's local dark/light threshold level.
 15. The electronic system of claim 8, wherein the error-correction equation stored in the memory comprises Reed-Solomon error correction equations.
 16. A computer-readable, non-transitory storage medium storing instructions that, when executed by a hardware processor of a symbol reader, causes the hardware processor to execute a method of error correction for a two-dimensional (2D) symbol designed for optical reading by the symbol reader, the 2D symbol having a plurality of cells of a designated first color and a designated second color which cells are arranged in a two-dimensional matrix; the 2D symbol further having a plurality of codewords at specified locations within the symbol, each codeword comprising at least one specified group of cells; the plurality of codewords comprising a first plurality of codewords storing data indicated by the pattern of first and second color cells in the codeword, and a second plurality of error-correction (EC) codewords derived from the data codewords and providing redundancy for the data represented by the data codewords; the method comprising: optically reading, by an optical scanner of the symbol reader, the plurality of codewords in the symbol; determining a location for a codeword which is optically ambiguous; marking in an error correction (EC) equation the location of the optically ambiguous codeword within the symbol; and executing the EC equation to correct errors in the read plurality of codewords.
 17. The computer-readable, non-transitory storage medium of claim 16, wherein the method further comprises determining the location for the codeword which is optically ambiguous by: determining a location for a codeword which displays a level of contrast between the first color and the second color which is insufficient for an unambiguous decoding of the codeword by the symbol reader.
 18. The computer-readable, non-transitory storage medium of claim 16, wherein the method further comprises determining the location for the codeword which is optically ambiguous by: selecting a codeword location based on a standards-established set of codeword locations within the symbol; and performing a contrast analysis on the codeword at the selected location, wherein the contrast analysis identifies a minimum interior contrast level for the selected codeword.
 19. The computer-readable, non-transitory storage medium of claim 18, wherein the method further comprises: identifying a respective minimum interior contrast level for each codeword in the symbol; and flagging as optically ambiguous a plurality of codewords with the lowest minimum interior contrast levels among all the codewords in the symbol, up to a specified number of codewords.
 20. The computer-readable, non-transitory storage medium of claim 18, wherein performing the contrast analysis on the codeword comprises: (i) determining a dark/light threshold level, wherein the dark/light threshold level is indicative of a reflectance above which a cell is assessed as being of the first color and below which a cell is assessed as being of the second color; (ii) determining a level of difference between the reflectance of each cell of the codeword and the dark/light threshold level; and (iii) determining the minimum interior contrast level for the codeword by determining, among all the cells within the codeword, a specific cell with a lowest level of difference between the reflectance of the specific cell and the dark/light threshold level. 